Can Angela Merkel govern as a minority government?

Coalitions tend to be brutal to minor partners, as they have in Britain under a similar Conservative-Liberal setup. The FDP was wiped out, leaving Merkel without a partner. The SPD suffered themselves when in a grand coalition with Merkel, and are probably better in Opposition biding their time. That leaves the Greens and the Communists. I cannot imagine DDR-born Merkel working with the Communists, and the Greens may not wish to go the same way as the FDP and wipe out themselves compromising with a Conservative. A Green ministry or two - say in agriculture, recycling and energy - may be a tempting bait to join the coalition though.

I don't think the SPD, the Greens and the Communists can form a grand coalition themselves, and Merkel is popular as a steady pair of hands. Her greatest threat comes from the Right, because of her willingness to bail out troublesome EU states in the Mediterranean. She can probably rely on the Centre-Left abstaining on critical issues.

This is an interesting election, since it is one likely scenario in Britain in 2015.

I gather they usually have some sort of coalition over there. Depends which of the minor parties she feels would be most useful and sympathetic to any proposed legislation that her government would want to pass.

She has for 2 terms.

Yes.